A cylindrical structure having an elliptic horizontal section is extremely graceful in shape and has a great strength. Hence, such a structure offers a novel feeling and a beautiful appearance, and thus, is greatly expected to be popular. In response to such a demand from this viewpoint, the applicant of the present invention previously filed Japanese Patent Application No. 2002-371121 which is titled “METHOD FOR DESIGNING OF APPROXIMATE ELLIPTICAL STRUCTURE AND THE SAME”, and Japanese Patent Laid-Open No. 2004-169527.
FIG. 1 is a perspective view of an elliptical structure (A) whose periphery is shaped like an ellipse over its full circumference (shown in FIG. 1 of the above described Application). FIG. 2 is a plan view of the elliptical structure (A), showing its outlined ellipse obtained as a result of mathematical calculation using an elliptic equation by means of a manual operation, a computer or the like. It is provided with a major axis (M) and a minor axis (N) on the coordinates x and y (i.e., its center lines) and is a (whole) outline (B) equivalent to the elliptic outline curve as the entire circumference formed by combining partial outlines (b1), (b2), (b3) and (b4) in a first quadrant (I), a second quadrant (II), a third quadrant (III) and a fourth quadrant (IV), respectively. This elliptic curve is symmetrical with respect to the major axis (M) and the minor axis (N).
However, an elliptic curve which shapes such an ellipse as described above is a quadratic curve which is characterized in that the sum of the distances from a specific point thereon to the two focuses of the ellipse is constant. When an elliptic curve is drawn, two coordinate points which are to be on the elliptic curve may be connected to each other with a single straight line as a convenient method, or with a polygonal line approximate to the elliptic curve. However, in order to connect the two coordinate points with a polygonal line, the distance between the two coordinate points must be finely divided and minute polygonal-line components must be drawn, so that they can be connected to one another. Therefore, in order to obtain an approximate elliptic curve, complex computations and operations are required. Thus, using such an approximate elliptic curve which is thus obtained means that it requires intricate calculations inevitably in designing an elliptical structure. Hence, it is not efficient, economical and feasible in drawing, land-surveying on a building site and fabricating building members.
Therefore, if an approximate elliptic curve is considered as a synthesis of circular segments and is drawn so as to be an ellipse which approximates a real ellipse, then a circle is determined depending upon its center and radius. Hence, such an elliptic curve is easy to design and draw, so that it is pointed out that an elliptical building can be practically and economically constructed. Herein, a method for this is disclosed.
Specifically, in FIG. 3 (showing a main part of FIG. 3 in Japanese Patent Laid-Open No. 2004-169527 described above), in order to obtain an outline (B1) which approximates the above described outline (B), a first fixed point (C1) is established outside of the elliptical structure (A). From here, a straight-line segment (L0) having a predetermined fixed length is drawn through an intersection point (o) of the minor axis (N) and the major axis (M) up to a farthest end point (P0) of the minor axis (N). With use of the first fixed point (C1) as the center and a first straight-line segment (L1) having the same length as that of the straight-line segment (L0) as the radius, an angle α1 is set at the first fixed point (C1), and then, a first circular segment (d1) is set from the point (P0) to a point (P1). Next, a second fixed point (C2) is established on the first straight-line segment (L1). At this second fixed point (C2), an angle α2 is set, and with use of the second fixed point (C2) as the center and a second straight-line segment (L2) as the radius, a second circular segment (d2) following the first circular segment (d1) is set from the point (P1) to a point (P2).
Similarly, circular segments are further set one by one in the above described way, an nth fixed point (Cn) established on a (Pn-1), (Cn-1) line equivalent to an (n-1)th straight-line segment (Ln-1) comes onto the major axis (M). With use of an (n-1)th fixed point (Cn-1) as the center and the (n-1)th straight-line segment (Ln-1) as the radius, a circle is drawn, and it intersects the major axis (M). This intersection point corresponds to a point (P5) in the example of FIG. 3.